Which of the following integers, when rounded to the nearest thousand, results in 2,000?
- A. 2,567
- B. 1,499
- C. 1,097
- D. 1,601
Correct Answer & Rationale
Correct Answer: d
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
Other Related Questions
What is 0.3 percent of 90?
- A. 0.027
- B. 0.27
- C. 0.3
- D. 2.7
Correct Answer & Rationale
Correct Answer: B
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
Multiplying a certain nonzero number by 0.01 gives the same result as dividing the number by
- A. 100
- B. 10
- C. 1/10
- D. 1/100
Correct Answer & Rationale
Correct Answer: A
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
At the Crest Coffee Shop, the cost of a plain bagel was $0.75 last year. This year the cost of a plain bagel is $0.90. By what percent did the cost of a plain bagel increase from last year to this year?
- A. 10%
- B. 15%
- C. 17%
- D. 20%
Correct Answer & Rationale
Correct Answer: D
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
Of the following, which is closest to (2,12/15 - 1/10) ÷ 16/6 ?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.